Let \(\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+5 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{c}}=\hat{\mathrm{i}}-4 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\) be three vectors. Let \(\vec{r}\) be a vector perpendicular to both \(\vec{b}, \vec{c}\) and \(\vec{r}, \vec{a}=11\). Then the vector among the following that is perpendicular to \(\vec{r}\) is

1. A \(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\)
2. B \(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}\)
3. C \(\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}\)
4. D \(\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}\)